How the fuck do you know what other people are going to do when the light is out or broken without communicating with them in some way?

Um. Because we have laws. As in, ways people are supposed to drive, even when the lights are out. I don't need to talk to everyone around me to figure out if they're going to follow the law because I'm going to assume they will like I do 99% of the time when I'm driving. I mean, do you do that at every stoplight you encounter? "Hey man, quick question. You gonna stop at this red light and go when it turns green? Okay just checking, thanks!" No? Then why would you do it now? I mean, you do realize that there are like, standard driving rules here, right? As in, legal rules for when people do and do not go at dysfunctional stoplights?

That being said, of course you need to look for other cars as you begin to move through the intersection to make sure you're not going to hit anybody, but that requires 0 communication with other drivers. I'm still trying to figure out what exactly you're trying to signal to somebody and how you expect them to understand it.

Or at least looking at their cars rather than your phone?

That's completely different from trying to use hand signals (that are only known to you and that you're, for some reason, assuming everyone else is just going to magically understand). I still don't see any reason to look at other cars while we're all sitting perfectly motionless, but you should, of course, be looking at the light. Which clearly OP was since they took a picture of it ;)